# How do you solve k-5/12=-3/10?

Feb 3, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{60}$ to eliminate the fraction and keep the equation balanced. Eliminating the fraction will make solving the problem easier to do. $\textcolor{red}{6}$ is the lowest common denominator of the two fractions.

$\textcolor{red}{60} \left(k - \frac{5}{12}\right) = \textcolor{red}{60} \times - \frac{3}{10}$

$\left(\textcolor{red}{60} \times k\right) - \left(\textcolor{red}{60} \times \frac{5}{12}\right) = \cancel{\textcolor{red}{60}} 6 \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}$

$60 k - \left(\cancel{\textcolor{red}{60}} 5 \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}}}\right) = - 18$

$60 k - 25 = - 18$

Next, add $\textcolor{red}{25}$ to each side of the equation to isolate the $k$ term while keeping the equation balanced:

$60 k - 25 + \textcolor{red}{25} = - 18 + \textcolor{red}{25}$

$60 k - 0 = 7$

$60 k = 7$

Now, divide each side of the equation by $\textcolor{red}{60}$ to solve for $k$ while keeping the equation balanced:

$\frac{60 k}{\textcolor{red}{60}} = \frac{7}{\textcolor{red}{60}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{60}}} k}{\cancel{\textcolor{red}{60}}} = \frac{7}{60}$

$k = \frac{7}{60}$